On an extension of the Kato-Voigt perturbation theorem for substochastic semigroups and its application

The aim of this paper is to discuss some recent developments of the perturb ation method introduced first by Kato for the Kolmogoroff equation and late r extended by Voigt and Arlotti to deal with a range of problems related to the solvability of the so-called Master Equation. The paper consists of tw o parts. In the first we recall and unify some abstract results on generati on of substochastic semigroups. In the second we perform a detailed analysi s of an equation from the polymer degradation theory to demonstrate a numbe r of possible generation cases.